# Chemistry and the Scientific Method | General Chemistry 1

## Scientific Method and Notation

**Scientific method:**

The scientific method is an empirical approach to problem-solving in science. It involves making observations, forming hypotheses, conducting experiments, collecting data, and drawing conclusions. Successful hypotheses may lead to the development of scientific theories.

**Scientific notation:**

Scientific notation is a way to express very large or very small numbers in a concise form.

In scientific notation, a number is written as *N* x 10* ^{n}*, where

*N*is a number between 1 and 10, and

*n*is a positive or negative integer.

850,000,000 = 8.5 x 10

^{8}in scientific notation

0.0000023 = 2.3 x 10^{-6 }in scientific notation

## States and Classification of Matter

**States of matter:**

Matter exists in three primary states: solid, liquid, and gas.

- Solids have a fixed volume and shape, with particles arranged in an ordered lattice.
- Liquids have a fixed volume but no specific shape, with particles free to move but held together by forces.
- Gases have neither fixed volume nor shape, with particles moving freely throughout the container.

**Phase changes:**

Phase changes involve the transition between different states of matter.

gas → liquid: condensation

gas → solid: deposition

liquid → solid: freezing

liquid → gas: boiling

solid → gas: sublimation

solid → liquid: melting

**Classification of matter:**

Matter can be classified as either a substance or a mixture.

- A substance has a definite composition and distinct properties, differing from other substances.
- A mixture consist of two or more substances, each retaining its identity, and can be homogeneous (uniform throughout) or heterogeneous. Mixtures can be separated using physical properties like filtration, distillation, or chromatography.

## The Properties of Matter

**Chemistry and matter:**

Chemistry is the study of matter and the changes it undergoes. Matter can be described by its properties, which may be quantitative (measured and expressed with a number) or qualitative (descriptive without numerical values).

**Physical vs. chemical properties:**

Physical properties can be observed or measured without changing the identity of the substance.

Chemical property is a property that are determined only as the result of a chemical process, where the original substance transforms into a new substance.

Physical properties: color, physical state, melting point, boiling point

Chemical properties: flammability, combustibility, oxidation states, enthalpy of formation

**Intensive vs. extensive properties:**

Intensive properties are independent of the amount of substance present.

Extensive properties are directly proportional to the amount of matter.

Intensive properties: density, color, temperature, hardness, melting point

Extensive properties: masse, volume, weight, length

## The International System of Units

**SI base units**

The International System of Units (SI) is the preferred system of units used in scientific work. SI units provide a standardized way to measure physical quantities and ensure consistency across scientific disciplines. There are seven fundamental SI base units:

- Length ⇒ meter = m
- Mass ⇒ kilogram = kg
- Temperature ⇒ kelvin = K
- Time ⇒ second = s
- Electric current ⇒ ampere = A
- Amount of substance ⇒ mole = mol
- Luminous intensity ⇒ candela = cd

**Prefixes used with SI units**

Prefixes are used in the metric system to denote multiples or subdivisions of SI units. Common prefixes for SI units include:

peta- (= P) ⇒ 10^{15}

tera- (= T) ⇒ 10^{12}

giga- (= G) ⇒ 10^{9}

mega- (= M) ⇒ 10^{6}

kilo- (= k) ⇒ 10^{3}

hecto- (= h) ⇒ 10^{2}

deca- (= da) ⇒ 10^{1}

deci- (= d) ⇒ 10^{-1}

centi- (= c) ⇒ 10^{-2}

milli- (= m) ⇒ 10^{-3}

micro- (= m) ⇒ 10^{-6}

nano- (= n) ⇒ 10^{-9}

pico- (= p) ⇒ 10^{-12}

femto- (= f) ⇒ 10^{-15}

## Fundamental Units: Mass, Length, & Temperature

**Mass:**

Mass is the amount of matter in an object and is measured in kilograms (kg) in the International System of Units (SI). One kilogram is equivalent to 2.205 pounds (lb).

Mass is distinct from weight, which is the force exerted by gravity on an object. Mass is constant regardless of an object's location, while weight varies depending on the gravitational field strength.

**Length:**

The meter (m) is the standard unit of length in the SI system. One meter is equivalent to 39.37 inches (in). The meter is defined as the distance traveled by light in a vacuum in 1/299,792,458 of a second.

**Temperature (T)**

Temperature can be measured in either the Kelvin scale (SI unit: K) or the Celsius scale (°C). The Kelvin scale is widely used in scientific contexts, while the Celsius scale is commonly used in everyday life. The relationship between Celsius and Kelvin temperatures is given by:

T (in K) = T (in °C) + 273.15

The Fahrenheit scale (°F) is also used, particularly in the United States, and the conversion from Celsius to Fahrenheit is:

T (in °F) = $\frac{9}{5}$ x T (in °C) + 32.0

## Derived Units: Volume, Density, & Energy

**Volume and density:**

The derived SI unit for volume is the cubic meter (m^{3}), but a more convenient measure is the liter (L).

1L = 1 dm^{3} and 1 m^{3} = 1000 L

Density (d) is the ratio of mass to volume and is typically expressed in kg.m^{-3}

*d* = $\frac{\mathrm{m}}{\mathrm{V}}$

m = mass (in kg)

V = volume (in m^{3})

**Energy and power:**

Energy (E) is the ability to cause a change in a physical system and is measured in joules (J), equivalent to kg.m^{2}.s^{-2}

The law of conservation of energy states that the total energy remains constant: E_{total} = E_{k} + E_{p} = constant

Kinetic Energy (E_{k}): energy associated with a moving object

E_{k} = $\frac{1}{2}$ mv^{2}

m =mass of the object (in kg)

v = velocity of the object (in m.s^{-1})

Potential Energy (E_{p}): energy of an object due to its location relative to a reference point. If the ground is the reference point:

E_{p} = mgh

m = mass (in kg)

g = the gravitational acceleration constant = 9.81 m.s^{-2} (on Earth)

h = the height (in m)

Power is the rate at which energy is produced or utilized and is measured in watts (W), equivalent to J.s^{-1}

## Uncertainty in Measurement

**Precision vs. accuracy:**

- Precision refers to the degree of agreement between replicate measurements. It indicates how close these measurements are to each other.
- Accuracy refers to how close a measurement or result is to the true or accepted value. Percentage error can be used to measure accuracy:

% error = $\left|\frac{\mathrm{average}\mathrm{value}-\mathrm{true}\mathrm{value}}{\mathrm{true}\mathrm{value}}\right|\times 100$

**Significant figures:**

Significant figures are the meaningful digits in a measured or calculated value, representing the uncertainty of the measurement. Rules for determining significant figures include:

- Non-zero digits are always significant.
- Any zeros between two significant digits are significant.
- Zeros to the left of the first non-zero digit are not significant.
- Zeros to the right of the last non-zero digit are significant if the number contains a decimal point.
- Zeros to the right of the last non-zero digit in a number without a decimal point may or may not be significant ⇒ scientific notation should be used to avoid ambiguity in such cases.

0.0

51has 2 significant figures

0.0510has 3 significant figures

5.100x 10^{3}has 4 significant figures

**Exact numbers:**

Exact numbers are quantities that can be counted or defined exactly, such as the number of objects. They have an infinite number of significant figures and do not limit the number of significant figures in a calculated result.

10 persons in a room ⇒ exact number ⇒ infinite number of significant figures

## Rounding Numbers

**Addition and subtraction:**

- Count the number of significant figures in the decimal portion of each number.
- Perform the addition or subtraction as usual.
- The final answer cannot have more significant figures to the right of the decimal point than any of the original numbers.

5.05 – 3.229 = 1.821

5.05 ⇒ 2 digits after the decimal point

3.229 ⇒ 3 digits after the decimal point

The final answer cannot have more than 2 digits after the decimal point and is therefore rounded to 1.82

**Multiplication and division:**

- Count the number of significant figures of each number.
- Perform the multiplication or division as usual.
- The number of significant figures in the final answer is determined by the original number that has the smallest number of significant figures.

2.1 x 0.0568 = 0.11928

2.1 ⇒ 2 significant figures

0.0568 ⇒ 3 significant figures

The final answer must have 2 significant figures and is therefore rounded to 0.12

## Dimensional Analysis

**Conversion factor:**

A conversion factor is a fraction where the same quantity is expressed in different units in the numerator and denominator, and it equals 1.

$\frac{3600\mathrm{s}}{1\mathrm{hour}}$ is the conversion factor to convert hours to seconds

**Dimensional analysis:**

Dimensional analysis involves using conversion factors to convert between different units while maintaining the same quantity. It ensures consistency and accuracy in calculations by manipulating quantities with their associated units.

Convert 2.0 m^{3}in liters:Conversion factors: $\frac{1000{\mathrm{dm}}^{3}}{1{\mathrm{m}}^{3}}$ and $\frac{1\mathrm{L}}{1{\mathrm{dm}}^{3}}$

Dimensional analysis: 2.0 m

^{3}x $\frac{1000{\mathrm{dm}}^{3}}{1{\mathrm{m}}^{3}}$ x $\frac{1\mathrm{L}}{1{\mathrm{dm}}^{3}}$ = 2000 L

Answer: 2.0 m^{3}= 2000 L

Convert 50 miles.hour^{-1}in m.s^{-1}:Conversion factors: $\frac{1.61\mathrm{km}}{1\mathrm{mile}}$ ; $\frac{1000\mathrm{m}}{1\mathrm{km}}$ ; $\frac{1\mathrm{hour}}{3600\mathrm{s}}$

Dimensional analysis: 50 miles.hour

Answer: 50 miles.hour^{-1}= $\frac{50\mathrm{miles}}{1\mathrm{hour}}$ x $\frac{1.61\mathrm{km}}{1\mathrm{mile}}$ x $\frac{1000\mathrm{m}}{1\mathrm{km}}$ x $\frac{1\mathrm{hour}}{3600\mathrm{s}}$ = 22.4 m.s^{-1}^{-1}= 22.4 m.s^{-1}

**Dimensional analysis method of problem solving:**

- Identify the given information, including units.
- Identify the information needed in the answer, including units.
- Find a relationship between the known information and needed answer and plan a strategy for conversion.
- Solve the problem using dimensional analysis.
- Check the reasonableness of the calculated answer with a rough estimate.

### Check your knowledge about this Chapter

Multiply the decimal number by 10 raised to the power indicated.

1.23 x 10^{3} = 1.23 x 1,000 = 1,230

1.23 x 10^{-3} = 1.23 x 0.001 = 0.00123

When adding or subtracting numbers in scientific notation, the exponents must be the same.

- Adjust the powers of 10 in the 2 numbers so that they have the same exponent.
- Add or subtract the decimal parts.
- Rewrite the result in scientific notation.

- Group the decimal parts and multiply them.
- Add the exponents.
- Rewrite the result in scientific notation.

Step 1: group the decimal parts and divide them.

Step 2: add the exponents of the numerators, subtract the result by the exponents of the denominators.

Step 3: rewrite the result in scientific notation.

The 2 temperature scales used in chemistry are the Celsius scale (°C), and the absolute or Kelvin scale (K). Outside of scientific circles, the Fahrenheit temperature scale is the most widely used in the United States.

We use the following equation to convert a temperature from units of degrees Celsius to Kelvins: K = °C + 273.15

Density is the ratio of mass to volume.

The volume of a substance is equal to the mass divided by the density of the substance.

The SI unit of mass is kg, that of volume is m^{3}, and that of density is kg.m^{-3}.

A joule (J) is equivalent to kg.m^{2}.s^{-2} in SI units.

The kinetic energy of an object is equal to half of its mass multiplied by the velocity squared.

The potential energy of an object relative to a reference point is equal to its mass (in kg) multiplied by the gravitational acceleration constant (9.81 m.s^{-2} on Earth) multiplied by the height of the object relative to the reference point (in m).

During any process, energy is neither created nor destroyed. Energy can be converted from one form to another or transferred from one system to another, but the total amount of energy never changes.

Due to the law of conservation of energy, E_{total} = E_{kinetic} + E_{potential} = constant

Power can be defined as the rate at which energy is produced or used. This quantity is expressed in watt (W) which is equivalent to J.s^{-1}.

Accuracy refers to how close a measurement/result is to the actual value while precision refers to how close a series of replicate measurements are to one another.

- Non-zero digits are always significant
- Any zeros between two significant digits are significant
- Zeros to the left of the first non-zero digit are not significant
- Zeros to the right of the last non-zero digit are significant if the number contains a decimal point

- Count the number of significant figures in the decimal portion of each number
- Add or subtract in the normal fashion
- The final answer cannot have more significant figures to the right of the decimal point than any of the original numbers

- Count the number of significant figures of each number
- Multiply or divide in the normal fashion
- The number of significant figures in the final answer is determined by the original number that has the smallest number of significant figures

Dimensional analysis is a technique used to convert the value of a physical quantity from one system of units to another system of units, while keeping the same quantity.

There are 7 fundamental dimensions in terms of which the dimensions of all other physical and chemical quantities may be expressed: length, mass, temperature, time, electric current, amount of substance, and luminous intensity.

- 2 physical quantities can only be compared if they have the same dimension
- 2 physical quantities can only be added or subtracted if they have the same dimensions
- The dimensions of the multiplication or division of 2 quantities are given by the multiplication or division of their dimensions of these 2 quantities

The principle of homogeneity states that the terms of an equation will have the same dimension on both sides. This principle is based on the fact that only physical quantities having the same dimension can be compared, added or subtracted.

A conversion factor is a fraction in which the same quantity is expressed one way in the numerator and another way in the denominator. It is used to change one set of units into another without changing the value.

Since the numerator and denominator of conversion factor express the same quantity, this fraction is always equal to 1.